Congling Qiu
My area of research is number theory. I study algebraic solutions of polynomial equations with symmetry. I mainly use tools from algebraic geometry and automorphic forms.
Recently I developed interests in the experimental and computational aspects of this field. Check some of my recent works (partly with Wei Zhang at MIT) arXiv:2209.09736, arXiv:2310.20600, arXiv:2310.20600, which are the papers 6,7,8 below. Also check the workshop I organized (with other organizers) at the Institute for Computational and Experimental Research in Mathematics.
I obtained my Ph.D. in mathematics from Princeton University in 2020 under the supervision of Shou-Wu Zhang. Then, I was a Gibbs Assistant Professor (aka Postdoc) at Department of Mathematics, Yale University, while I was supported by NSF (National Science Foundation) grant DMS #2000533. Now I'm a postdoc at MIT.
Email: qiuc AT mit DOT edu,
qiucongling AT gmail DOT com.
(Photo by my wife)
Publications & Preprints
My talks (not updated for a while...) on them are here.
Automorphic L-functions of central vanishing orders at least 3. In preparation.
Non-vanishing of Ceresa cycles for modular curves (with Wanlin Li). In preparation.
Theta correspondence and Springer correspondence (with Ma, Jia-Jun, Zhiwei Yun and Jialiang Zou). In preparation.
Zero-cycles on squares of elliptic curves and Shimura curves. In preparation.
Faber--Pandharipande Cycles vanish for Shimura curves. Preprint.
Finiteness properties for Shimura curves and modified diagonal cycles. arXiv:2310.20600.
Appendix to 3.1 of ``Finiteness properties for Shimura curves and Modified diagonal cycles"
Vanishing results in Chow groups for the modified diagonal cycles II: Shimura curves (with Wei Zhang). arXiv:2310.19707.
Vanishing results in Chow groups for the modified diagonal cycles (with Wei Zhang). Tunisian Journal of Mathematics. arXiv:2209.09736
Appendix to "Vanishing results in Chow groups for the modified diagonal cycles"
Linearity on ordinary Siegel moduli schemes and joint unlikely almost intersections. arXiv:2209.05018
Generic Hecke algebra and theta correspondence over finite fields (with Jia-Jun Ma, Jialiang Zou). Advances in Mathematics. arXiv:2208.00431
Modularity of arithmetic special divisors for unitary Shimura varieties (with an appendix by Yujie Xu). Forum of Mathematics, Sigma, recommended by referees for publication and under revision. arXiv:2204.13457
Modularity and heights of CM cycles on Kuga-Sato varieties. Algebra & Number Theory, recommended by referees for publication and under revision. arXiv:2105.12561
The Gross-Zagier-Zhang formula over function fields. Mathematische Annalen. arXiv:1903.02092
The Manin-Mumford conjecture and the Tate-Voloch conjecture for a product of Siegel moduli spaces. Algebra & Number Theory. arXiv:1903.02089
Teaching
Yale University
Spring 2023, MATH 610: Introduction to Arithmetic Geometry
Fall 2022, MATH 115: Integral Calculus (two sections)
Spring 2022, MATH 354: Number Theory
Fall 2021, MATH 717: Arithmetic of Cyclotomic Fields
Fall 2021, MATH 373: Algebraic Number Theory
Spring 2021, MATH 370: Fields and Galois Theory
Spring 2021, MATH 353: Intro to Representation Theory
Fall 2020, MATH 310: Introduction to Complex Analysis
Princeton University
Fall 2018, MATH 202: Linear Algebra with Applications
Seminars
I co-organized the Yale Algebra and Number Theory Seminar.
Spring 2022 (with Elad Zelingher)
Fall 2021 (with Elad Zelingher)
Spring 2021 (with Yifeng Liu, Elad Zelingher)
Fall 2020 (with Yifeng Liu, Elad Zelingher)